# NCERT Solutions Class 8 Maths Chapter 15

## NCERT Solutions for Class 8 Mathematics Chapter 15 – Introduction of Graphs

Mathematics is the study of numbers and their applications. To score well in Mathematics, students should practice a lot of problems. More and more practice in mathematics will make students confident about their performance and make them better learners.

The chapter Introduction to Graphs is included in the Algebra section of Mathematics. The important topics of this chapter are different types of graphs like linear graphs, the method used to draw different types of graphs, and their applications. After completing this chapter, students will be able to manage large data in the form of graphs. They will also be able to draw different types of graphs with ease.

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NCERT Solutions for Class 8 Mathematics Chapter 15 is the perfect resource to cover this chapter in a detailed manner. Everything from the top to the end of the chapter is covered in our NCERT solutions. This would help students develop a strong conceptual understanding of this chapter and they will be able to apply it in their real life. It also helps students recall quickly and retain most of the concepts covered in this chapter. Hence, students learn at a fast pace.

You can get our NCERT Solutions for Class 8 Mathematics Chapter 15 from the Extramarks website by registering on it and searching for the required study material. All the content on the website is designed keeping in mind all the latest trends of the CBSE syllabus. All questions and exercises are up to the mark. It also has various curriculum-oriented activities to make Mathematics a fun experience. Therefore, students start enjoying Mathematics after referring to NCERT solutions from the Extramarks website.

### Key Topics Covered In NCERT Solutions for Class 8 Mathematics Chapter 15

Graphs play a significant role in mathematics. This chapter talks about the essential components of graphs and their applications. To understand and interpret large data, students should be thorough with this chapter. All the points required in the study of schematic diagrams are covered in this chapter. After reading about this chapter from NCERT Solutions for Class 8 Mathematics Chapter 15, students can understand different types of graphs accurately. They will also be able to plot different graphical diagrams.

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The numerous questions and exercises given in our NCERT Solutions for Class 8 Mathematics Chapter 15 require students to use their critical thinking ability and apply a wide range of formulas they have learned.

Introduction

Graphs are nothing but scale-wise plotting of big data in structured matter. You are already aware of graphs from the lower classes.

In this chapter, we will particularly talk about different types of graphs. They are as follows:

• A bar graph

A bar graph is used to show a comparison among.

• A pie graph

A pie graph is used to compare the different parts of a whole circle.

• A histogram

A histogram is a bar graph that shows data in intervals.

• A line graph

A line graph shows data that changes continuously.

Students can read more about different types of graphs and their real-life applications from our NCERT Solutions for Class 8 Mathematics Chapter 15, available on the Extramarks website.

Linear graphs

A number of line segments are joined together to form a linear graph. There are different steps to plotting linear graphs. They are as follows:

1. Finding the location of a point
2. Plotting its required coordinates

Students need to specifically find a point on the graph using scales. Then they can plot the obtained coordinates on the graph. In this way, linear graphs are plotted.

For students to better understand the working of linear graphs, we have provided multiple examples with illustrations of actual scenarios in our NCERT solution study materials. Register on the Extramarks website to get full access to our NCERT Solutions for Class 8 Mathematics Chapter 15.

Some applications

A number of dependent and independent variables are associated with the graph plotting. Based on it, there are various applications for plotting a graph. They include:

• Quantity and Cost
• Principal and Simple interest
• Time and Distance

Students can easily solve these sums using the dependent and independent variables and jump to conclusions. Thus, it makes graphical problems easy and approachable.

This section is the most important in our NCERT Solutions for Class 8 Mathematics Chapter 15 as it covers a lot of applications-oriented examples of using various forms of graphs.

Summary

You have learned all about graphs from this chapter.

You have covered different types of graphs like:

• A bar graph: Is used to show the comparison between the different categories
• A pie graph: Is used to compare parts of a whole
• A histogram: It is a kind of bar graph that shows data in intervals
• A line graph: It shows data that continuously changes over a period of time

You have learnt about the steps to plot a linear graph. They are as follows:

1. Finding the location of a point
2. Plotting its required coordinates

• Quantity and Cost
• Principal and Simple Interest
• Time and Distance

Along with full chapter notes, our NCERT Solutions for Class 8 Mathematics Chapter 15 also provides succinct revision notes. Students can rely on these revision guides for a quick last-minute revision before their exams.

## NCERT Solutions for Class 8 Mathematics Chapter 15: Exercise & Answer Solutions

We have covered all the exercises and answer solutions given in the NCERT textbook in our NCERT solutions for class 8 mathematics chapter 15. Our study solutions provide a variety of questions covering every aspect of the chapter, which will help students clear their concepts efficiently and solve problems accurately within a short period of time. As a result, they will gain the confidence to solve different sets of questions. Subject matter experts design the NCERT solutions. Hence, students can trust our study resources to give them the highest quality solutions.

Click on the below links to view exercise-specific questions and solutions for NCERT Solutions for Class 8 Mathematics Chapter 15:

Class 8 Mathematics Introduction to Graphs – Exercise & Answer Solutions

 Chapter 15 – Introduction to Graphs All Exercises Exercise 15.1 Question and Solutions Exercise 15.2 Questions and Solutions Exercise 15.3 Questions and Solutions

Extramarks has many other study materials for students preparing for Class 1 to Class 12 exams. Along with Class 8 Mathematics solutions, students can explore NCERT Solutions for all primary and secondary classes. Click on the links given below to access our NCERT Solutions:

### NCERT Exemplar Class 8 Mathematics

NCERT Exemplar Class 8 Mathematics book has a lot of popularity among the aspirants of competitive examinations due to its quality content and wide range of questions. The set of questions is designed as per the latest CBSE curriculum. The book is receiving constant positive feedback from parents and teachers.

One can trust all sets of questions as subject matter experts design them. Students should consider every question important as each question has a new core concept covered. Hence, students learn something from every question they solve.

NCERT Exemplar is a trusted resource for students to include in their study material. The wide variety of questions will help boost students’ confidence. Hence, they will be able to solve the maximum number of questions accurately within a stipulated time.

### Key Features of NCERT Solutions for Class 8 Mathematics Chapter 15

To score well, one must revise the concepts thoroughly. Hence, NCERT Solutions for Class 8 Mathematics Chapter 15 offers a complete solution for all problems. The key features included in the Class 8 Mathematics Chapter 15 are as follows:

• The NCERT solutions are prepared by subject matter experts from the Mathematics stream. They curate solutions by referring to many additional reference books and preparing questions and answers that align with the CBSE exams.
• It is designed in a quick-to-learn format, thereby allowing students to easily retain the concepts. The study notes include many tips for memorising formulas and doing mental calculations to increase speed.
• After completing the NCERT Solutions for Class 8 Mathematics Chapter 15, students can solve questions based on all the basic and advanced topics related to graphs.

Q.1 The following graph shows the temperature of a patient in a hospital, recorded every hour.
(a) What was the patient’s temperature at 1 p.m.?
(b) When was the patient’s temperature 38.5° C?
(c) The patient’s temperature was the same two times during the period given. What were these two times?
(d) What was the temperature at 1.30 p.m.? How did you arrive at your answer?
(e) During which periods did the patients’ temperature showed an upward trend? Ans-

(a) The patient’s temperature was 36.5°C at 1 p.m.
(b) At 12 noon, the patient’s temperature was 38.5°C.
(c) The two times when the patient’s temperature was same, were 1 p.m. and 2 p.m.
(d) The temperature at 1:30 p.m. is 36.5°C.
(e) The patient’s temperature showed an upward trend during the following periods: 9 a.m. to 10 a.m., 10 a.m. to 11 a.m., 2 p.m. to 3 p.m.

Q.2 The following line graph shows the yearly sales figures for a manufacturing company.
(a) What were the sales in (i) 2002 (ii) 2006?
(b) What were the sales in (i) 2003 (ii) 2005?
(c) Compute the difference between the sales in 2002 and 2006.
(d) In which year was there the greatest difference between the sales as compared to its previous year? Ans-

(a)
(i) The sales in 2002 were ₹ 4 crores.
(ii) The sales in 2006 were ₹ 8 crores.
(b)
(i) The sales in 2003 were ₹ 7 crores.
(ii) The sales in 2005 were ₹ 10 crores.
(c)
(i) The difference between the sales in 2002 and 2006 = ₹ (8 − 4) crores = ₹ 4 crores
(d) For finding the greatest difference between the sales as compared to its previous year, we have to find compare all the years.
Therefore, the difference between the sales of the year 2006 and 2005 = ₹ (10 − 8) crores = ₹ 2 crores
Difference between the sales of the year 2005 and 2004 = ₹ (10 − 6) crores = ₹ 4 crores
Difference between the sales of the year 2004 and 2003 = ₹ (7 − 6) crore = ₹ 1 crore
Difference between the sales of the year 2003 and 2002 = ₹ (7 − 4) crores = ₹ 3 crores
Hence, the difference was the maximum in the year 2005 as compared to its previous year 2004.

Q.3 For an experiment in Botany, two different plants, plant A and plant B were grown under similar laboratory conditions. Their heights were measured at the end of each week for 3 weeks. The results are shown by the following graph.
(a) How high was Plant A after (i) 2 weeks (ii) 3 weeks?
(b) How high was Plant B after (i) 2 weeks (ii) 3 weeks?
(c) How much did Plant A grow during the 3rd week?
(d) How much did Plant B grow from the end of the 2nd week to the end of the 3rd week?
(e) During which week did Plant A grow most?
(f) During which week did Plant B grow least?
(g) Were the two plants of the same height during any week shown here? Specify. Ans-

(a)
(i) The height of plant A was 7 cm after 2 weeks.
(ii) The height of plant A was 9 cm after 3 weeks.
(b)
(i) The height of plant B was 7 cm after 2 weeks.
(ii) The height of plant B was 10 cm after 3 weeks.
(c) The growth of plant A during 3rd week = 9 cm − 7 cm = 2 cm
(d) The growth of plant B from the end of the 2nd week to the end of the 3rd week = 10 cm − 7 cm = 3 cm
(e) The growth of plant A during 1st week = 2 cm − 0 cm = 2 cm
The growth of plant A during 2nd week = 7 cm − 2 cm = 5 cm
The growth of plant A during 3rd week = 9 cm − 7 cm = 2 cm
Therefore, plant A grew the most, i.e. 5 cm, during the 2nd week.

(f) The growth of the plant B during 1st week = 1 cm − 0 cm = 1 cm
The growth of the plant B during 2nd week = 7 cm − 1 cm = 6 cm
The growth of plant B during 3rd week = 10 cm − 7 cm = 3 cm
Therefore, plant B grew the least, during the 1st week.

(g) The two plants were of the same height during the 2nd week.

Q.4 The following graph shows the temperature forecast and the actual temperature for each day of a week.
(a) On which days was the forecast temperature the same as the actual temperature?
(b) What was the maximum forecast temperature during the week?
(c) What was the minimum actual temperature during the week?
(d) On which day did the actual temperature differ the most from the forecast temperature? Ans-

(a) The forecast temperature was same as the actual temperature on Tuesday, Friday, and Sunday.
(b) The maximum forecast temperature during the week was 35°C.
(c) The minimum actual temperature during the week was 15°C.
(d) The actual temperature differs the most from the forecast temperature on Thursday.

Q.5 Use the tables below to draw linear graphs.

(a) The number of days a hill side city received snow in different years.

 Year 2003 2004 2005 2006 Days 8 10 5 12

(b) Population (in thousands) of men and women in a village in different years.

 Year 2003 2004 2005 2006 2007 Number of Men 12 12.5 13 13.2 13.5 Number of Women 11.3 11.9 13 13.6 12.8

Ans-

1.  Year 2003 2004 2005 2006 Days 8 10 5 12 2.  Year 2003 2004 2005 2006 2007 Number of Men 12 12.5 13 13.2 13.5 Number of Women 11.3 11.9 13 13.6 12.8
3. Q.6 A courier-person cycles from a town to a neighbouring suburban area to deliver a parcel to a merchant. His distance from the town at different times is shown by the following graph.
(a) What is the scale taken for the time axis?
(b) How much time did the person take for the travel?
(c) How far is the place of the merchant from the town?
(d) Did the person stop on his way? Explain.
(e) During which period did he ride fastest? Ans-

(a) Scale taken for the time axis is 4 units = 1 hour
(b)

$\mathrm{The}\mathrm{person}\mathrm{took}3\frac{1}{2}\mathrm{hours}\mathrm{to}\mathrm{travel}.$

(c) The merchant is 22 km far from the town.
(d) Yes, the person stopped on his way from 10 a.m. to 10: 30 a.m. It is clearly shown by the horizontal line in the graph.
(e) From 8 a.m. to 9 a.m., the person travelled the maximum distance. So, the person’s ride was the fastest between 8 a.m. and 9 a.m.

Q.7 Can there be a time-temperature graph as follows? Justify your answer. Ans-

(i) As the temperature can increase with the increase in time, so it can be a time−temperature graph..
(ii) As the temperature can decrease with the decrease in time, so it can be a time−temperature graph.
(iii) Since different temperatures at the same time are not possible, so it cannot be a time−temperature graph.
(iv) As same temperature at different times is possible, so it can be a time−temperature graph.

Q.8 Plot the following points on a graph sheet. Verify if they lie on a line
(a) A(4, 0), B(4, 2), C(4, 6), D(4, 2.5)
(b) P(1, 1), Q(2, 2), R(3, 3), S(4, 4)
(c) K(2, 3), L(5, 3), M(5, 5), N(2, 5)

Ans- When we plot the points on the graph and then join them, it can be observed that they lie on the same line. It can be observed from the graph that the points P, Q, R and S lie on the same line. When all the points are joined, it can be observed that they don’t lie on the same line.

Q.9 Draw the line passing through (2, 3) and (3, 2). Find the coordinates of the points at which this line meets the x-axis and y-axis.

Ans- The line passing through (2, 3) and (3,2) meets the x-axis and y-axis are (5, 0) and (0, 5).

Q.10 Write the coordinates of the vertices of each of these adjoining figures. Ans-

The coordinates of the vertices in the given figure are as follows.

OABC: O (0, 0), A (2, 0), B (2, 3), C (0, 3)

PQRS: P (4, 3), Q (6, 1), R (6, 5), S (4, 7)

MLK : K (10, 5), L (7, 7), M (10, 8)

Q.11 State whether True or False. Correct that are false.
(i) A point whose x coordinate is zero and y-coordinate is non-zero will lie on the y-axis.
(ii) A point whose y coordinate is zero and x-coordinate is 5 will lie on y-axis.
(iii) The coordinates of the origin are (0, 0).

Ans-

(i) True
(ii) False: The point whose y-coordinate is zero and x-coordinate is 5 will lie on x-axis.
(iii) True

12. Draw the graphs for the following tables of values, with suitable scales on the axes.

(a) Cost of apples

 Number of apples 1 2 3 4 5 Cost 5 10 15 20 25

(b) Distance travelled by a car

 Time (in hours) 6a.m. 7 a.m. 8 a.m. 9 a.m. Distances (in km) 40 80 120 160
1. How much distance did the car cover during the period 7.30 a.m. to 8 a.m.?
2. What was the time when the car had covered a distance of 100 km since it’s start?

(c) Interest on deposits for a year.

 Number of apples 1 2 3 4 5 Cost 5 10 15 20 25
1. Does the graph pass through the origin?
2. Use the graph to find the interest on ₹ 2500 for a year.
3. To get an interest of ₹ 280 per year, how much money should be deposited?

Ans-

(a)

 Number of apples 1 2 3 4 5 Cost 5 10 15 20 25

Scale:
X-axis, 1 unit = 10 apples
Y-axis, 1 unit = Rs 10
A graph of the given data is as follows. (b)

 Time (in hours) 6a.m. 7 a.m. 8 a.m. 9 a.m. Distances (in km) 40 80 120 160

Scale:
X-axis, 2 units = 1 hour
Y-axis, 2 units = 40 km
A graph of the given data is as follows. 1. The car covered a distance of 20 km during the period 7:30 a.m. to 8 a.m.
2. The car covered a distance of 100 km since its start at 7:30 a.m.

(c)

 Deposit (in Rs) 1000 2000 3000 4000 5000 Simple Interest (in Rs) 80 160 240 320 400 1. Yes, the graph passes through the origin.
2. The interest on Rs 2500 for a year is Rs 200.
3. To get an interest of Rs 280 per year, Rs 3500 should be deposited.

Q.13 Draw a graph for the following.

(i)

 Side of square 2 3 3.5 5 6 Perimeter 8 12 14 20 24

Is it a linear graph?

(ii)

 Side of square (in cm) 2 3 3.5 5 6 Area (in cm2) 4 9 16 25 36

Is it a linear graph?

Ans-

(i)

 Side of square 2 3 3.5 5 6 Perimeter 8 12 14 20 24 Scale:
X axis: 1 unit = 5 cm
Y axis: 1 unit = 5 cm
It is a linear graph.

(ii)

 Side of square (in cm) 2 3 3.5 5 6 Area (in cm2) 4 9 16 25 36 Scale:
X axis: 1 unit = 1 cm
Y axis: 1 unit = 5 cm2
It is not a linear graph.

## 1. How important is NCERT Class 8 Mathematics Chapter 15?

The chapter contains all the basic concepts of graphs required in higher Mathematics. Thus, it builds students’ conceptual understanding in graphs and their plotting, which will aid in solving all types of schematic questions quickly and accurately. As a result, it is one of the most important chapters of Class 8 Mathematics.

## 2. How can I improve my understanding of Mathematics?

Mathematics is a subject which requires a lot of practice. One can improve the understanding of Mathematics by solving as many questions as possible. You can find a bunch of questions in our NCERT Solutions for Class 8 Mathematics Chapter 15 on the Extramarks website. It will help build up your confidence in Mathematics as you will practice various questions.

## 3. What is a bar graph?

The rectangular columns present a bar graph. The height or length is proportional to the value that they represent.